基于三维Taylor多项式建立局域海洋地磁场模型

在海洋磁力测量中,波浪和风等外界因素的变化会对磁力测量数据在垂直空间上产生影响,而二维Taylor多项式在建立局域海洋地磁场模型时没有考虑高度变化对模型的影响。针对这一问题,提出使用三维Taylor多项式完全展开法来构建局域海洋地磁场模型,通过模拟某海域水下球体磁场,仿真船载磁力测量数据,分析两种模型截断阶数的选择、完全与不完全展开的区别和模型边界效应等问题。实验表明,在顾及高度变化的情况下,三维Taylor多项式模型能更详细地反映海洋磁力异常的分布情况,且较好地改善了边界效应。     

地震波正演模拟中无单元Galerkin法初探

无单元Galerkin法作为一种新型有限元开始应用于地震勘探领域.地震波正演模拟结果的好坏取决于基函数类型、节点分布、节点编号方式、稳定条件以及边界条件等因素,通过对各个因素的分析可知:基函数的阶数越高,结果精度越高,但数据量和运算量就越大;不同的基函数联合使用时,会带来数值计算上的误差;节点可以不均匀分布,但必须满足空间采样要求;合理的节点编号有利于节约数据量和减少运算量;采用衰减边界条件,能有效克服无单元Galerkin法在边界上处理的难点.以上分析结果,对无单元Galerkin法在地震波正演模拟中的应用具有一定的指导意义.     

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基坑开挖对临近地铁隧道影响的两阶段分析方法

城市高层建筑施工中进行基坑开挖必然引起周围地层移动,从而造成临近地铁隧道纵向不均匀沉降,最终对地铁正常运营产生严重影响。针对目前该领域存在的三维有限元建模复杂及计算耗时的缺点,考虑基坑开挖引起的坑底和四周坑壁土体同时卸荷产生的影响,提出了基坑开挖对临近地铁隧道纵向变形影响的两阶段分析方法。首先计算基坑开挖作用在地铁隧道上的附加荷载,然后基于Winkler地基模型建立地铁隧道纵向变形影响的基本微分方程,根据Galerkin方法将该方程转换为一维有限元方程进行计算,同时研究了不同隧道埋深、距离基坑开挖现场远近、不同地基土质和不同隧道外径等因素对隧道纵向变形的影响。结合大型三维有限元数值模拟以及现场实测数据将计算结果进行了对比,得到较好的一致性。成果可为合理制定基坑开挖对临近地铁隧道的保护措施提供一定的理论依据     

ECMWF集合预报系统对秦岭周边地区降水确定性预报的性能分析

尽管确定性预报不是集合预报系统(EPS)的主要目的和应用方向,但其每一个成员的预报表现决定了集合预报系统的预报性能,集合平均也是实际预报业务的一个重要参考指标。为此,利用2013~2015年5~10月的欧洲中期天气预报中心(ECMWF)集合预报系统的降水预报资料,CMORPH(NOAA Climate Prediction Center Morphing Method)卫星与全国3×10~4余个自动气象观测站的逐小时降水量融合资料,研究ECMWF集合预报系统对秦岭周边地区逐日降水的控制预报、成员预报、集合平均的预报能力,并探索提高降水集合平均预报性能的有效方法。主要结论如下:(1)无论是集合平均还是控制预报,整体上都较好的刻画了秦岭周边地区降水的空间形态,比较而言,控制预报能够更好的表现了降水的方差变化。(2)泰勒分析表明,集合平均的降水方差随预报时效增加单调减小,控制预报的方差变化随预报时效的增长振荡较小,其相关系数略优于集合平均。(3)技巧评分表明,集合平均使小雨(降水发生频次)的预报偏差显著增加,增大了空报率;使大雨以上的降水预报偏差减小,增大了漏报率,从而使得大多数情况下,集合平均TS(Threat Score)、ETS(Equitable Threat Score)评分低于控制及扰动成员预报。分析认为这主要是由于降水这一要素的偏态分布特性引起的。(4)集合平均的显著贡献在于能够较好的指示可能发生降水的空间位置。通过阈值限定,调整预报偏差,减少(增大)其对小雨(暴雨)的预报频率,能够使集合平均的TS、ETS评分大幅度提升,预报技巧显著优于成员预报和控制预报。目前,预报偏差Bias订正方法已成功应用于陕西省精细化格点预报系统中。     

Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas where no water is present, as standard numerical methods may fail in the presence of these areas. These equations also have still water steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. In this paper we propose a high order discontinuous Galerkin method which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. A simple positivity-preserving limiter, valid under suitable CFL condition, will be introduced in one dimension and then extended to two dimensions with rectangular meshes. Numerical tests are performed to verify the positivity-preserving property, well-balanced property, high order accuracy, and good resolution for smooth and discontinuous solutions.     

非共振二阶椭圆型方程解的存在唯一性

利用Galerkin逼近方法和minimax原理，证明了非线性非共振椭圆型方程弱解的存在唯一性。     

海平面上升对海岸潮差响应的理论解析

应用海湾和半封闭矩形海域改进的Taylor问题的解研究海平面上升对M2分潮旋转潮波系统及沿岸潮差的变化.将南黄海概化为一等深矩形海域,初步研究在海平面上升3 m和5 m条件下该海域旋转潮波系统的演化趋势,继而分析沿岸潮差变化特征.初步分析研究表明:随着海平面上升,该海域M2分潮的无潮点有向东南方向偏移的趋势,受此影响,沿岸潮差呈现不同的变化特征,靠近无潮点的左侧及湾顶海岸变化明显,而远离无潮点的右侧及湾顶海岸则变化不大.     

A temporal stable isotopic (δ18O, δD,d‐excess) comparison in glacier meltwater streams,Taylor Valley,Antarctica

In this paper, we describe the importance of hyporheic dynamics within Andersen Creek and Von Guerard Stream, Taylor Valley, Antarctica, from the 2010–2011 melt season using natural tracers. Water collection started at flow onset and continued, with weekly hyporheic‐zone sampling. The water δ¹⁸O and δD values were isotopically lighter in the beginning and heavier later in the season. D‐excess measurements were used as an indicator of mixing because an evaporative signature was evident and distinguishable between 2 primary end‐members (glacier meltwater and hyporheic zone). Hyporheic‐zone influence on the channel water was variable with a strong control on streamwater chemistry, except at highest discharges. This work supports previous research indicating that Von Guerard Stream has a large, widespread hyporheic zone that varies in size with time and discharge. Andersen Creek, with a smaller hyporheic zone, displayed hyporheic‐zone solute interaction through the influence from subsurface hypersaline flow. Overall, the evolution of Taylor Valley hyporheic‐zone hydrology is described seasonally. In mid‐December, the hyporheic zone is a dynamic system exchanging with the glacier meltwater in the channel, and with diminishing flow in January, the hyporheic zone drains back into the channel flow also impacting stream chemistry. This work adds new information on the role of hyporheic zone–stream interaction in these glacier meltwater streams.